Long-term adaptation of epistatic genetic networks

Gene networks are likely to govern most traits in nature. Mutations at these genes often show functional epistatic interactions that lead to complex genetic architectures and variable fitness effects in different genetic backgrounds. Understanding how epistatic genetic systems evolve in nature remains one of the great challenges in evolutionary biology. Here we combine an analytical framework with individual-based simulations to generate novel predictions about long-term adaptation of epistatic networks. We find that relative to traits governed by independently evolving genes, adaptation with epistatic gene networks is often characterized by longer waiting times to selective sweeps, lower standing genetic variation, and larger fitness effects of adaptive mutations. This may cause epistatic networks to either adapt more slowly or more quickly relative to a nonepistatic system. Interestingly, epistatic networks may adapt faster even when epistatic effects of mutations are on average deleterious. Further, we study the evolution of epistatic properties of adaptive mutations in gene networks. Our results show that adaptive mutations with small fitness effects typically evolve positive synergistic interactions, whereas adaptive mutations with large fitness effects evolve positive synergistic and negative antagonistic interactions at approximately equal frequencies. These results provide testable predictions for adaptation of traits governed by epistatic networks and the evolution of epistasis within networks.     

Mutational neighbourhood and mutation supply rate constrain adaptation in Pseudomonas aeruginosa

Understanding adaptation by natural selection requires understanding the genetic factors that determine which beneficial mutations are available for selection. Here, using experimental evolution of rifampicin-resistant Pseudomonas aeruginosa, we show that different genotypes vary in their capacity for adaptation to the cost of antibiotic resistance. We then use sequence data to show that the beneficial mutations associated with fitness recovery were specific to particular genetic backgrounds, suggesting that genotypes had access to different sets of beneficial mutations. When we manipulated the supply rate of beneficial mutations, by altering effective population size during evolution, we found that it constrained adaptation in some selection lines by restricting access to rare beneficial mutations, but that the effect varied among the genotypes in our experiment. These results suggest that mutational neighbourhood varies even among genotypes that differ by a single amino acid change, and this determines their capacity for adaptation as well as the influence of population biology processes that alter mutation supply rate.     

The opportunity for canalization and the evolution of genetic networks

There has been a recent revival of interest in how genetic interactions evolve, spurred on by an increase in our knowledge of genetic interactions at the molecular level. Empirical work on genetic networks has revealed a surprising amount of robustness to perturbations, suggesting that robustness is an evolved feature of genetic networks. Here, we derive a general model for the evolution of canalization that can incorporate any form of perturbation. We establish an upper bound to the strength of selection on canalization that is approximately equal to the fitness load in the system. This method makes it possible to compare different forms of perturbation, including genetic, developmental, and environmental effects. In general, load that arises from mutational processes is low because the mutation rate is itself low. Mutation load can create selection for canalization in a small network that can be achieved through dominance evolution or gene duplication, and in each case selection for canalization is weak at best. In larger genetic networks, selection on genetic canalization can be reasonably strong because larger networks have higher mutational load. Because load induced through migration, segregation, developmental noise, and environmental variance is not mutation limited, each can cause strong selection for canalization.     

ESS gene expression of X-linked imprinted genes subject to sexual selection

We define ESS (Evolutionary Stable Strategy) conditions for the evolution of genomic imprinting at an X-linked locus. The system analysed is designed for mammalian imprinting in which X-linked genes typically undergo random X-inactivation and lack Y-linked homologues. We consider two models that map cellular gene expression to fitness in females subject to random X-inactivation. In the first model, female fitness is simply a function of the average gene expression across all cells. In the second model, each cell contributes independently to fitness, and female fitness is assessed as the average of these contributions across all cells. In both models, imprinting readily evolves when sexual selection favours different levels of gene expression in the two sexes. Imprinting is beneficial as it improves adaptation in both sexes. There are limits to the improvement in adaptation when sexual selection is strong and favours greater gene expression in males (the heterogametic sex). We also consider the consequences of an active Y-linked homologue on the evolution of imprinting. Our analysis suggests that restrictive conditions apply for the evolution of polymorphic ESSs at an X-linked imprinted loci.     

Escape from growth restriction in small colony variants of Salmonella typhimurium by gene amplification and mutation

Antibiotic resistance in bacteria is generally associated with fitness costs that often can be reduced by second-site compensatory mutations. Here, we examined how a protamine-resistant small colony variant of Salmonella typhimurium adapts to the growth reduction conferred by a resistance mutation in hemC (encoding a haem-biosynthesis enzyme). We show that adaptation occurs in a multi-step process where fitness is successively increased. Thus, the initial adaptive response was selection for an unstable gene amplification of the mutant hemC gene that provided a small fitness increase. Fitness was increased further by a mutation that restored HemC function in one gene copy, relaxing selection for the amplification. Subsequently, the amplification segregated back to the haploid state and even higher fitness. The end result was in most cases mutant strains with a hemC sequence different from that of the wild-type strain. These findings suggest that gene amplification facilitates adaptive evolution. A higher gene dosage increases the target size for compensatory mutations and improves fitness of the cell, thereby allowing an increase in the population size, further increasing the probability of a subsequent stable mutation. Our results provide a novel genetic basis for growth compensation in small colony variants.     

Frequency-dependent selection and the evolution of assortative mating

A long-standing goal in evolutionary biology is to identify the conditions that promote the evolution of reproductive isolation and speciation. The factors promoting sympatric speciation have been of particular interest, both because it is notoriously difficult to prove empirically and because theoretical models have generated conflicting results, depending on the assumptions made. Here, we analyze the conditions under which selection favors the evolution of assortative mating, thereby reducing gene flow between sympatric groups, using a general model of selection, which allows fitness to be frequency dependent. Our analytical results are based on a two-locus diploid model, with one locus altering the trait under selection and the other locus controlling the strength of assortment (a "one-allele" model). Examining both equilibrium and nonequilibrium scenarios, we demonstrate that whenever heterozygotes are less fit, on average, than homozygotes at the trait locus, indirect selection for assortative mating is generated. While costs of assortative mating hinder the evolution of reproductive isolation, they do not prevent it unless they are sufficiently great. Assortative mating that arises because individuals mate within groups (formed in time or space) is most conducive to the evolution of complete assortative mating from random mating. Assortative mating based on female preferences is more restrictive, because the resulting sexual selection can lead to loss of the trait polymorphism and cause the relative fitness of heterozygotes to rise above homozygotes, eliminating the force favoring assortment. When assortative mating is already prevalent, however, sexual selection can itself cause low heterozygous fitness, promoting the evolution of complete reproductive isolation (akin to "reinforcement") regardless of the form of natural selection.     

Natural selection fails to optimize mutation rates for long-term adaptation on rugged fitness landscapes

The rate of mutation is central to evolution. Mutations are required for adaptation, yet most mutations with phenotypic effects are deleterious. As a consequence, the mutation rate that maximizes adaptation will be some intermediate value. Here, we used digital organisms to investigate the ability of natural selection to adjust and optimize mutation rates. We assessed the optimal mutation rate by empirically determining what mutation rate produced the highest rate of adaptation. Then, we allowed mutation rates to evolve, and we evaluated the proximity to the optimum. Although we chose conditions favorable for mutation rate optimization, the evolved rates were invariably far below the optimum across a wide range of experimental parameter settings. We hypothesized that the reason that mutation rates evolved to be suboptimal was the ruggedness of fitness landscapes. To test this hypothesis, we created a simplified landscape without any fitness valleys and found that, in such conditions, populations evolved near-optimal mutation rates. In contrast, when fitness valleys were added to this simple landscape, the ability of evolving populations to find the optimal mutation rate was lost. We conclude that rugged fitness landscapes can prevent the evolution of mutation rates that are optimal for long-term adaptation. This finding has important implications for applied evolutionary research in both biological and computational realms.     

The distribution of beneficial and fixed mutation fitness effects close to an optimum

The distribution of the selection coefficients of beneficial mutations is pivotal to the study of the adaptive process, both at the organismal level (theories of adaptation) and at the gene level (molecular evolution). A now famous result of extreme value theory states that this distribution is an exponential, at least when considering a well-adapted wild type. However, this prediction could be inaccurate under selection for an optimum (because fitness effect distributions have a finite right tail in this case). In this article, we derive the distribution of beneficial mutation effects under a general model of stabilizing selection, with arbitrary selective and mutational covariance between a finite set of traits. We assume a well-adapted wild type, thus taking advantage of the robustness of tail behaviors, as in extreme value theory. We show that, under these general conditions, both beneficial mutation effects and fixed effects (mutations escaping drift loss) are beta distributed. In both cases, the parameters have explicit biological meaning and are empirically measurable; their variation through time can also be predicted. We retrieve the classic exponential distribution as a subcase of the beta when there are a moderate to large number of weakly correlated traits under selection. In this case too, we provide an explicit biological interpretation of the parameters of the distribution. We show by simulations that these conclusions are fairly robust to a lower adaptation of the wild type and discuss the relevance of our findings in the context of adaptation theories and experimental evolution.     

The SOS response increases bacterial fitness,but not evolvability,under a sublethal dose of antibiotic

Exposure to antibiotics induces the expression of mutagenic bacterial stress–response pathways, but the evolutionary benefits of these responses remain unclear. One possibility is that stress–response pathways provide a short-term advantage by protecting bacteria against the toxic effects of antibiotics. Second, it is possible that stress-induced mutagenesis provides a long-term advantage by accelerating the evolution of resistance. Here, we directly measure the contribution of the Pseudomonas aeruginosa SOS pathway to bacterial fitness and evolvability in the presence of sublethal doses of ciprofloxacin. Using short-term competition experiments, we demonstrate that the SOS pathway increases competitive fitness in the presence of ciprofloxacin. Continued exposure to ciprofloxacin results in the rapid evolution of increased fitness and antibiotic resistance, but we find no evidence that SOS-induced mutagenesis accelerates the rate of adaptation to ciprofloxacin during a 200 generation selection experiment. Intriguingly, we find that the expression of the SOS pathway decreases during adaptation to ciprofloxacin, and this helps to explain why this pathway does not increase long-term evolvability. Furthermore, we argue that the SOS pathway fails to accelerate adaptation to ciprofloxacin because the modest increase in the mutation rate associated with SOS mutagenesis is offset by a decrease in the effective strength of selection for increased resistance at a population level. Our findings suggest that the primary evolutionary benefit of the SOS response is to increase bacterial competitive ability, and that stress-induced mutagenesis is an unwanted side effect, and not a selected attribute, of this pathway.     

The evolution of mutation rate in finite asexual populations

In this article, we model analytically the evolution of mutation rate in asexual organisms. Three selective forces are present. First, everything else being equal, individuals with higher mutation rate have a larger fitness, thanks to the energy and time saved by not replicating DNA accurately. Second, as a flip side, the genome of these individuals is replicated with errors that may negatively affect fitness. Third, and conversely, replication errors have a potential benefit if beneficial mutations are to be generated. Our model describes the fate of modifiers of mutation rate under the three forces and allows us to predict the long-term evolutionary trajectory of mutation rate. We obtain three major results. First, in asexuals, the needs for both adaptation and genome preservation are not evolutionary forces that can stabilize mutation rate at an intermediate optimum. When adaptation has a significant role, it primarily destabilizes mutation rate and yields the emergence of strong-effect mutators. Second, in contrast to what is usually believed, the appearance of modifiers with large mutation rate is more likely when the fitness cost of each deleterious mutation is weak, because the cost of replication errors is then paid after a delay. Third, in small populations, and even if adaptations are needed, mutation rate is always blocked at the minimum attainable level, because the rate of adaptation is too slow to play a significant role. Only populations whose size is above a critical mass see their mutation rate affected by the need for adaptation.     

Robustness to noise in gene expression evolves despite epistatic constraints in a model of gene networks

Stochastic noise in gene expression causes variation in the development of phenotypes, making such noise a potential target of stabilizing selection. Here, we develop a new simulation model of gene networks to study the adaptive landscape underlying the evolution of robustness to noise. We find that epistatic interactions between the determinants of the expression of a gene and its downstream effect impose significant constraints on evolution, but these interactions do allow the gradual evolution of increased robustness. Despite strong sign epistasis, adaptation rarely proceeds via deleterious intermediate steps, but instead occurs primarily through small beneficial mutations. A simple mathematical model captures the relevant features of the single‐gene fitness landscape and explains counterintuitive patterns, such as a correlation between the mean and standard deviation of phenotypes. In more complex networks, mutations in regulatory regions provide evolutionary pathways to increased robustness. These results chart the constraints and possibilities of adaptation to reduce expression noise and demonstrate the potential of a novel modeling framework for gene networks.     

The evolution of stress-induced hypermutation in asexual populations

Numerous empirical studies show that stress of various kinds induces a state of hypermutation in bacteria via multiple mechanisms, but theoretical treatment of this intriguing phenomenon is lacking. We used deterministic and stochastic models to study the evolution of stress-induced hypermutation in infinite and finite-size populations of bacteria undergoing selection, mutation, and random genetic drift in constant environments and in changing ones. Our results suggest that if beneficial mutations occur, even rarely, then stress-induced hypermutation is advantageous for bacteria at both the individual and the population levels and that it is likely to evolve in populations of bacteria in a wide range of conditions because it is favored by selection. These results imply that mutations are not, as the current view holds, uniformly distributed in populations, but rather that mutations are more common in stressed individuals and populations. Because mutation is the raw material of evolution, these results have a profound impact on broad aspects of evolution and biology.     

Augmenting Microarray Data with Literature-Based Knowledge to Enhance Gene Regulatory Network Inference

Gene regulatory networks are a crucial aspect of systems biology in describing molecular mechanisms of the cell. Various computational models rely on random gene selection to infer such networks from microarray data. While incorporation of prior knowledge into data analysis has been deemed important, in practice, it has generally been limited to referencing genes in probe sets and using curated knowledge bases. We investigate the impact of augmenting microarray data with semantic relations automatically extracted from the literature, with the view that relations encoding gene/protein interactions eliminate the need for random selection of components in non-exhaustive approaches, producing a more accurate model of cellular behavior. A genetic algorithm is then used to optimize the strength of interactions using microarray data and an artificial neural network fitness function. The result is a directed and weighted network providing the individual contribution of each gene to its target. For testing, we used invasive ductile carcinoma of the breast to query the literature and a microarray set containing gene expression changes in these cells over several time points. Our model demonstrates significantly better fitness than the state-of-the-art model, which relies on an initial random selection of genes. Comparison to the component pathways of the KEGG Pathways in Cancer map reveals that the resulting networks contain both known and novel relationships. The p53 pathway results were manually validated in the literature. 60% of non-KEGG relationships were supported (74% for highly weighted interactions). The method was then applied to yeast data and our model again outperformed the comparison model. Our results demonstrate the advantage of combining gene interactions extracted from the literature in the form of semantic relations with microarray analysis in generating contribution-weighted gene regulatory networks. This methodology can make a significant contribution to understanding the complex interactions involved in cellular behavior and molecular physiology.     

The adaptive value of epigenetic mutation: Limited in large but high in small peripheral populations

The fate of populations during range expansions, invasions and environmental changes is largely influenced by their ability to adapt to peripheral habitats. Recent models demonstrate that stable epigenetic modifications of gene expression that occur more frequently than genetic mutations can both help and hinder adaptation in panmictic populations. However, these models do not consider interactions between epimutations and evolutionary forces in peripheral populations. Here, we use mainland–island mathematical models and simulations to explore how the faster rate of epigenetic mutation compared to genetic mutations interacts with migration, selection and genetic drift to affect adaptation in peripheral populations. Our model focuses on cases where epigenetic marks are stably inherited. In a large peripheral population, where the effect of genetic drift is negligible, our analyses suggest that epimutations with random fitness impacts that occur at rates as high as 10^–3 increase local adaptation when migration is strong enough to overwhelm divergent selection. When migration is weak relative to selection and epimutations with random fitness impacts decrease adaptation, we find epigenetic modifications must be highly adaptively biased to enhance adaptation. Finally, in small peripheral populations, where genetic drift is strong, epimutations contribute to adaptation under a wider range of evolutionary conditions. Overall, our results suggest that epimutations can change outcomes of adaptation in peripheral populations, which has implications for understanding conservation and range expansions and contractions, especially of small populations.     

A new method to uncover signatures of divergent and stabilizing selection in quantitative traits

While it is well understood that the pace of evolution depends on the interplay between natural selection, random genetic drift, mutation, and gene flow, it is not always easy to disentangle the relative roles of these factors with data from natural populations. One popular approach to infer whether the observed degree of population differentiation has been influenced by local adaptation is the comparison of neutral marker gene differentiation (as reflected in FST) and quantitative trait divergence (as reflected in QST). However, this method may lead to compromised statistical power, because FST and QST are summary statistics which neglect information on specific pairs of populations, and because current multivariate tests of neutrality involve an averaging procedure over the traits. Further, most FST-QST comparisons actually replace QST by its expectation over the evolutionary process and are thus theoretically flawed. To overcome these caveats, we derived the statistical distribution of population means generated by random genetic drift and used the probability density of this distribution to test whether the observed pattern could be generated by drift alone. We show that our method can differentiate between genetic drift and selection as a cause of population differentiation even in cases with FST=QST and demonstrate with simulated data that it disentangles drift from selection more accurately than conventional FST-QST tests especially when data sets are small.     

Evolution of carrying capacity in evolution experiments focusing on a single locus on the Escherichia coli chromosome

We performed a series of evolution experiments, the results of which illustrated the relationship between mutations and increased carrying capacity (K). Performing an evolution experiment with repeated cycles of mutation by PCR and selection makes it possible to obtain results over shorter culture durations than in methods reported previously relying on spontaneous mutation and selection. We constructed random mutant populations of Escherichia coli in which members differed only in part of the genomic copy of the glutamine synthetase gene and performed daily serial transfer culture where the populations were in K-selected environments. The value of K in this system was increased by 10(5)- to 10(8)-fold relative to the parent clone, which was achieved by four randomly introduced mutations. This method can be applied to any gene and will be useful for analyzing a number of important issues in evolutionary biology.     

Comparing artificial and natural selection in rate of adaptation to genetic stress in Aspergillus nidulans

In an experimental study of adaptation to negative pleiotropic effects of a major fungicide resistance mutation in the filamentous fungus Aspergillus nidulans we have investigated the relative effectiveness of artificial selection vs. natural selection on the rate of compensatory evolution. Using mycelial growth rate as a fitness measure, artificial selection involved the weekly transfer of the fastest growing sector onto a fresh plate. Natural selection was approximated by transferring random samples of all the spores produced by the mycelium. Fungicide resistant and fungicide sensitive haploid and diploid strains were used in an evolution experiment over 10 weekly transfers, which is equivalent to 1200 cell cycles. Two different environmental conditions were applied: a constant fungicide-free environment and a weekly alternation between presence and absence of fungicide. Results show that for all strains and conditions used the transfer of a random sample of all spores leads to more rapid adaptation than the transfer of the visually 'fittest' sector. The rates of compensatory evolution in the constant and the alternating environment did not differ. Moreover, haploid strains tend to have a higher rate of adaptation than isogenic diploid strains.     

The Time Scale of Evolutionary Innovation

A fundamental question in biology is the following: what is the time scale that is needed for evolutionary innovations? There are many results that characterize single steps in terms of the fixation time of new mutants arising in populations of certain size and structure. But here we ask a different question, which is concerned with the much longer time scale of evolutionary trajectories: how long does it take for a population exploring a fitness landscape to find target sequences that encode new biological functions? Our key variable is the length, of the genetic sequence that undergoes adaptation. In computer science there is a crucial distinction between problems that require algorithms which take polynomial or exponential time. The latter are considered to be intractable. Here we develop a theoretical approach that allows us to estimate the time of evolution as function of We show that adaptation on many fitness landscapes takes time that is exponential in even if there are broad selection gradients and many targets uniformly distributed in sequence space. These negative results lead us to search for specific mechanisms that allow evolution to work on polynomial time scales. We study a regeneration process and show that it enables evolution to work in polynomial time.     

Mutation-biased adaptation in a protein NK model

Evolutionary trends responsible for systematic differences in genome and proteome composition have been attributed to GC:AT mutation bias in the context of neutral evolution or to selection acting on genome composition. A possibility that has been ignored, presumably because it is part of neither the Modern Synthesis nor the Neutral Theory, is that mutation may impose a directional bias on adaptation. This possibility is explored here with simulations of the effect of a GC:AT bias on amino acid composition during adaptive walks on an abstract protein fitness landscape called an "NK" model. The results indicate that adaptation does not preclude mutation-biased evolution. In the complete absence of neutral evolution, a modest GC:AT bias of realistic magnitude can displace the trajectory of adaptation in a mutationally favored direction, to such a degree that amino acid composition is biased substantially and persistently. Thus, mutational explanations for evolved patterns need not presuppose neutral evolution.     

Nuclear–mitochondrial epistasis: a gene's eye view of genomic conflict

We use population genetic models to investigate the cooperative and conflicting synergistic fitness effects between genes from the nucleus and the mitochondrion. By varying fitness parameters, we examine the scope for conflict relative to cooperation among genomes and the utility of the “gene's eye view” analytical approach, which is based on the marginal average fitness of specific alleles. Because sexual conflict can maintain polymorphism of mitochondrial haplotypes, we can explore two types of evolutionary conflict (genomic and sexual) with one epistatic model. We find that the nuclear genetic architecture (autosomal, X‐linked, or Z‐linked) and the mating system change the regions of parameter space corresponding to the evolution by sexual and genomic conflict. For all models, regardless of conflict or cooperation, we find that population mean fitness increases monotonically as evolution proceeds. Moreover, we find that the process of gene frequency change with positive, synergistic fitnesses is self‐accelerating, as the success of an allele in one genome or in one sex increases the frequency of the interacting allele upon which its success depends. This results in runaway evolutionary dynamics caused by the positive intergenomic associations generated by selection. An inbreeding mating system tends to further accelerate these runaway dynamics because it maintains favorable host–symbiont or male–female gene combinations. In contrast, where conflict predominates, the success of an allele in one genome or in one sex diminishes the frequency of the corresponding allele in the other, resulting in considerably slower evolutionary dynamics. The rate of change of mean fitness is also much faster with positive, synergistic fitnesses and much slower where conflict is predominant. Consequently, selection rapidly fixes cooperative gene combinations, while leaving behind a slowing evolving residue of conflicting gene combinations at mutation–selection balance. We discuss how an emphasis on marginal fitness averages may obscure the interdependence of allelic fitness across genomes, making the evolutionary trajectories appear independent of one another when they are not.